# Properties

 Label 95370db Number of curves 6 Conductor 95370 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95370.dc1")

sage: E.isogeny_class()

## Elliptic curves in class 95370db

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95370.dc4 95370db1 [1, 0, 0, -2112596, 1181700240] [2] 1769472 $$\Gamma_0(N)$$-optimal
95370.dc3 95370db2 [1, 0, 0, -2135716, 1154506496] [2, 2] 3538944
95370.dc5 95370db3 [1, 0, 0, 1106864, 4351041860] [2] 7077888
95370.dc2 95370db4 [1, 0, 0, -5748216, -3782336004] [2, 2] 7077888
95370.dc6 95370db5 [1, 0, 0, 15132034, -24942381354] [2] 14155776
95370.dc1 95370db6 [1, 0, 0, -84428466, -298565760654] [2] 14155776

## Rank

sage: E.rank()

The elliptic curves in class 95370db have rank $$0$$.

## Modular form 95370.2.a.dc

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 6q^{13} - q^{15} + q^{16} + q^{18} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.